If I have an equation like $x^2+y^2+4z^2=10$, would the cylindrical equation then just be $r^2=10-4z^2$? I found this answer, but it just seems like it was too easy to find.
2026-03-26 18:57:53.1774551473
Converting a rectangular equation to cylindrical coordinates
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$$x^2 + y^2 + 4z^2 = 10$$ represents an ellipsoid centered at the origin in Cartesian coordinates. To express this equation in cylindrical coordinates, you can substitute $x$ and $y$ with their equivalent cylindrical coordinates, $r \cdot \cos(\theta)$ and $r \cdot \sin(\theta)$, respectively. The equation becomes:
$$( r \cdot \cos(\theta))^2 + (r \cdot \sin( \theta))^2 + 4z^2 = 10.$$
Simplifying this equation, we have:
$$r^2 + 4z^2 = 10.$$